I managed to produce the same picture as you, DrDre:
http://screenshotcomparison.com/comparison/138479
The algorithm matches the probability density function (PDF) of each image. If you do this with just the original color space, the colors will hardly mach. So the idea of the algorithm is to transform the color space and match the PDF again. The transformation of the color space is done by multiplying the picture with a rotation matrix. The algorithm does this N times. In this example I calculated 50 rotation matricies and used all of them to create the image in post #5. In the image of this post I still calculated 50 rotation matrices, but just used the first 49 of them to do the color transfer. In this image I used just one rotation.